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1、BSSMWorkshop PARTII Thesin2ψMethodUsingLaboratoryX-RaysJudithShackleton SchoolofMaterials,UniversityofManchesterThesin2ψMethod WhatareWeMeasuring?WemeasuretheELASTICStrain.WecandetermineMagnitudeofthestress,ItsdirectionItsnatureCompressiveortensileWeusetheplanesofthecrystallatt
2、iceasanatomicscale“straingauge”Thesin2ψMethod HowDoesitWork?WemeasureSTRAIN()notSTRESS()WeCALCULTESTRESSfromtheSTRAIN&theELASTICCONSTANTSWeusetheplanesd{hkl},ofthecrystallatticeasastraingaugeWecanmeasurethechangeind-spacing,dStrain==d/dChangesind-spacing withStressConsider
3、abarwhichisintensionThed-spacingsoftheplanesnormaltotheappliedstressincrease,asthestressistensileThed-spacingsoftheplanesparalleltotheappliedstressdecrease,duetoPoissonstrainMeasuringElastic& Inelastic StrainPrimarilywearemeasuringmacrostressesThisisauniformdisplacementofthelat
4、ticeplanesThesecauseaVERYSMALLshiftintheposition,theBraggangle2,ofthereflection&wecanmeasurethis(OnlyJust!!)Inelasticstressescausepeakbroadening,whichcanbemeasured.Thisisanextensivesubject,notcoveredhere.WhichMaterialsCan WeMeasure?Worksonanypoly-crystallinesolidwhichgivesahig
5、hangleBraggreflectionMetalsCeramics(noteasy!)Multi-phasematerialsNotusuallyappliedtopolymers,asnosuitablereflections,canaddametallicpowder,reportedintheliteratureWhyusethesin2 Method TheAdvantagesMostImportantAstressfreed-spacingisNOTrequiredforthebi-axialcasewhichisalmostalwa
6、ysusedOtheradvantagesLowcost(comparedwithneutrons&synchrotrons,butnotholedrilling)Non-destructive,unlikeholedrillingEasytodo&fairlyfoolproof(ifyouarecareful!!)DisadvantagesMostImportantSurfacemethodonly,X-raybeampenetrationdepth10to20microns,atbestFordepthprofilingmustelectro-p
7、olish,gives1-1.5mmOtherDisadvantagesAffectedbygrainsize,texture(preferredorientation)&surfaceroughnessDoesn’tworkonamorphousmaterials(obviously!!)BasicTheoryConsideraunitcube(quiteabigone!)embeddedinacomponentNotation,(ij)thestresscomponentactingonfaceiindirection(paralleltoa
8、xis)jBasicTheoryThenormalstressesactnormaltothecubefac
